CFSE of mixing

Therefore, according to this calculation, there is an excess CFSE (enthalpy) of mixing of about -1.6 kJ/(mole of olivine). Similarly, the formation of all intermediate olivines by mixing of Mg2Si04 and Fe2Si04 components results in an excess CFSE of mixing. This is illustrated in fig. 7.3. These results imply that there is a heat of mixing term and that the olivine series is not an ideal solid-solution of forsterite and fayalite. 

Figure 7.4 Excess CFSE of mixing for Mg2+-Ni2+ olivines of the forsterite-liebenber-gite series (see table 7.2).

This calculation shows that the formation of intermediate liebenbergite by mixing of Mg2Si04 and Ni2Si04 components is accompanied by an excess CFSE of mixing of -5.65 kJ/mole. These results suggest that Mg2+-Ni2+ olivines depart considerably from ideal solution behaviour (Bish, 1981). This is further demonstrated in fig. 7.4 by the compositional variation of excess CFSE of mixing for the suite of synthetic Mg2+-Ni2+ olivines for which site occupancy and CFSE data are available (table 7.2). 

It should be noted, however, that in a multisite substitution where cation ordering occurs, a heat of mixing term could arise even in the absence of a compositional variation of the CFSE. For example, the excess CFSE of mixing would increase to about -8.20 kJ/mole in solid-solution formation of the liebenbergite (Mg0 49Ni0 51)2SiO4, eq. (7.14), if the CFSE of Ni2+ ions in the Ml and M2 sites were to remain constant at -143.1 and -113.2 kJ/mole, respectively. 

A necessary condition for an ideal solid-solution behaviour is that there be zero heat of mixing in forming the solution from its components, eq. (7.6). This condition cannot be fulfilled when differences exist between CFSE s of cations in the end-member components and in the solid-solutions. 

Table 11.8 reveals that most spinels involving Fe (AFe .04) have the inverse structure. The d Fe ion will have a CFSE of zero for both tetrahedral and octahedral coordination, so if there is to be a site preference it will be due to the A(ll) ion. This is cleatly the case for NiFe204. for example, the Nr ion having an octahedral site preference energy of 86 kJ mol. In magnetite. Fe,04, both A and B ions are iron, with some in the +2 oxidation state and others in +3 Fe"Fe" 04. the f" Ft ion, octahedral coordination is more favorable than tetrahedral by about 13 kJ tiu>l, whieh, although only a modest amount, is apparently sufficient to invert the structure. In contrast, the similar oxide Mn]04 has the normal structure. In this instance, the Mn has no CFSE in either octahedral or tetrahedral fields, but d Mn shows a preference of 106 kJ mol for octahedral sites. For Q>,04. another mixed-valence oxide, there is an additional fiictor to take into account—Co is low... 

This differential CFSE factor is demonstrated by the formation of hortono-lite, (Mgo5Fe05)2Si04, by the mixing of forsterite and fayalite components. To a close approximation, Mg2+ and Fe2+ ions may be assumed to be randomly distributed in the olivine structure eq., (7.12), so that 0.5 Fe2+ ions per formula unit occupy each of the Ml and M2 positions. The CFSE s of the Fe2+ ion in the Ml and M2 sites of hortonolite are approximately -53.2 and -52.0 kJ/mole, respectively, and in fayalite the corresponding CFSE are -50.9 kJ/mole (Ml site) and -51.2 kJ/mole (M2 site) (eqs (5.2) and (5.3) table 5.16). The formation of hortonolite may be represented as follows ... 

Finally in this section, we note the remarkable prevalence of tetrahedral four-coordination in zinc(II) chemistry see Zinc Inorganic Coordination Chemistry), to an extent comparable with cobalt(II), although d enjoys no advantage from CFSE. Tetrahedrally bonded zinc(II) is found in many metalloenzymes see Zinc Enzymes) and can often be replaced by cobalt without loss of enzymatic activity. This can be attributed to d-p mixing. In tetrahedral symmetry Td), the nAxy,xz,yz and(n + l)Px,y,z orbitals each constitute a threefold-degenerate t2 set and become mixed. The LF t2 orbitals are thus lowered in energy, and the d configuration (where t2 is filled) is consequently stabilized. 

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